The Immigration and Nationality Act (INA) enables an immigrant to obtain a visa as a “special immigrant religious worker” if the immigrant meets certain statutory criteria, including that he has been “carrying on” religious work for at least the two years preceding the filing of the visa petition. This case presents the question whether a requirement imposed in the relevant regulation [8 CFR 204.5(m)] that this religious work have been carried on “in lawful immigration status” crosses the line from permissible statutory interpretation by the responsible agency to ultra vires regulation contrary to the clear intent of Congress..... [T]he District Court here concluded that the regulation is ultra vires because it contradicts the plain language of the INA..... For the reasons set forth below, we agree. We therefore will affirm the District Court’s order as to the invalidity of the regulation but will reverse and remand for further fact-finding on the remaining visa criteria.